31 citations · 149 across the 21 of their papers we have counts for
24 papers
Vietoris-Rips complexes of Platonic solids
Nada Saleh, Thomas Titz Mite, Stefan Witzel
We determine the homotopy type of the Vietoris-Rips complexes of the (vertex sets of the) platonic solids. The most interesting case is that the Vietoris-Rips complex of the dodeca…
Higher finiteness properties of arithmetic approximate lattices: The Rank Theorem for number fields
Tobias Hartnick, Stefan Witzel
We introduce geometric and homological finiteness properties for countable approximate groups via coarse geometry and then study these finiteness properties for S-arithmetic reduct…
Hyperbolic generalized triangle groups, property (T) and finite simple quotients
Pierre-Emmanuel Caprace, Marston Conder, Marek Kaluba +1
We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously know…
Strong Property (T), weak amenability and -cohomology in -buildings
Jean Lécureux, Mikael de la Salle, Stefan Witzel
We prove that cocompact (and more generally: undistorted) lattices on -buildings satisfy Lafforgue's strong property (T), thus exhibiting the first examples that are n…
Quasi-isometric diversity of marked groups
Ashot Minasyan, Denis Osin, Stefan Witzel
We use basic tools of descriptive set theory to prove that a closed set of marked groups has quasi-isometry classes provided every non-empty open subset…
Boundary Braids
Michael Dougherty, Jon McCammond, Stefan Witzel
The n-strand braid group can be defined as the fundamental group of the configuration space of n unlabeled points in a closed disk based at a configuration where all n points lie i…
Simple groups separated by finiteness properties
Rachel Skipper, Stefan Witzel, Matthew C. B. Zaremsky
We show that for every positive integer there exists a simple group that is of type but not of type . For these groups are the first k…
Classifying spaces from Ore categories with Garside families
Stefan Witzel
We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's…
On panel-regular ~A_2 lattices
Stefan Witzel
We study lattices on ~A_2 buildings that preserve types, act regularly on each type of edge, and whose vertex stabilizers are cyclic. We show that several of their properties, such…
The Basilica Thompson group is not finitely presented
Stefan Witzel, Matthew C. B. Zaremsky
We show that the Basilica Thompson group introduced by Belk and Forrest is not finitely presented, and in fact is not of type FP_2. The proof involves developing techniques for pro…
Tasting the SU(5) nature of supersymmetry at the LHC
Sylvain Fichet, Björn Herrmann, Yannick Stoll
We elaborate on a recently found SU(5) relation confined to the up-(s)quark flavour space, that remains immune to large quantum corrections up to the TeV scale. We investigate the…
Thompson groups for systems of groups, and their finiteness properties
Stefan Witzel, Matthew C. B. Zaremsky
We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson g…
CAT(0) cubical complexes for graph products of finitely generated abelian groups
Kim Ruane, Stefan Witzel
We show that every graph product of finitely generated abelian groups acts properly and cocompactly on a CAT(0) cubical complex. The complex generalizes (up to subdivision) the Sal…
A free subgroup in the image of the 4-strand Burau representation
Stefan Witzel, Matthew C. B. Zaremsky
It is known that the Burau representation of the 4-strand braid group is faithful if and only if certain matrices f and k generate a (non-abelian) free group. Regarding f and k as…
Local convexity in CAT(κ)-spaces
Kai-Uwe Bux, Stefan Witzel
Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a local property. We generalize this to CAT(0)-spaces and locally compact CAT(κ) spa…
The braided Thompson's groups are of type
Kai-Uwe Bux, Martin Fluch, Marco Marschler +2
We prove that the braided Thompson's groups and are of type , confirming a conjecture by John Meier. The proof involves showing that matching co…
The Brin-Thompson groups sV are of type F_\infty
Martin Fluch, Marco Marschler, Stefan Witzel +1
We prove that the Brin-Thompson groups sV, also called higher dimensional Thompson's groups, are of type F_\infty for all natural numbers s. This result was previously shown for s…
Brown's criterion in Bredon homology
Martin Fluch, Stefan Witzel
We translate Brown's criterion for homological finiteness properties to the setting of Bredon homology.
Abels's groups revisited
Stefan Witzel
We generalize a class of groups introduced by Herbert Abels to produce examples of virtually torsion free groups that have Bredon-finiteness length m-1 and classical finiteness len…
Finiteness Properties of Chevalley Groups over the Ring of (Laurent) Polynomials over a Finite Field
Stefan Witzel
In these notes we determine the finiteness length of the groups G(O_S) where G is an F_q-isotropic, connected, noncommutative, almost simple F_q-group and O_S is one of F_q[t], F_q…
Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem
Kai-Uwe Bux, Ralf Köhl, Stefan Witzel
We show that the finiteness length of an -arithmetic subgroup in a noncommutative isotropic absolutely almost simple group over a global function field is one less than…
Finiteness Properties of Chevalley Groups over the Laurent Polynomial Ring over a Finite Field
Stefan Witzel
We show that if G is a Chevalley group of rank n and F_q[t,t^{-1}] is the ring of Laurent polynomials over a finite field, then G(F_q[t,t^{-1}]) is of type F_{2n-1}. This bound is…
Finiteness Properties of Chevalley Groups over a Polynomial Ring over a Finite Field
Kai-Uwe Bux, Ralf Köhl, Stefan Witzel
It is known from work by H. Abels and P. Abramenko that for a classical Fq-group G of rank n the arithemetic lattice G(Fq[t]) of Fq[t]-rational points is of type Fn-1 provided that…
The sphericity of the Phan geometries of type Bn and Cn and the Phan-type theorem of type F4
Ralf Köhl, Stefan Witzel
We adapt and refine methods developed by Abramenko and Devillers--Köhl--Mühlherr in order to establish the sphericity of the Phan geometries of type B_n and C_n, and their generali…